Model Mathematics

Component: parameters

$L_m=L_prime_m-L_bK_1=k_1⁢CaK_m=k_m⁢Cak_m=k_1k_minus_1=k_1K_maxk_minus_m=k_minus_1g_prime_0=g_0g_prime_1=g_1$

Component: non_overlap

$Rbar_n=A_n⁢k_minus_11+K_1R_n=Rbar_n⁢alpha⁢L_mAbar_n=R_n⁢K_11+k_minus_1A_n=Abar_n⁢alpha⁢L_m$

Component: single_overlap

$dRbar_s_dt=-K_1⁢R_s+k_minus_1⁢A_s+g_prime_0+g_prime_1⁢V⁢U_sddtimeRbar_s=dRbar_s_dtddtimeR_s=dRbar_s_dt⁢alpha⁢L_m-Rbar_s⁢L_m⁢VifV>0dRbar_s_dt⁢alpha⁢L_m+2⁢Rbar_d-Rbar_s⁢L_m⁢|V|ifV<0dRbar_s_dt⁢alpha⁢L_motherwisedAbar_s_dt=K_1⁢R_s+-f-k_minus_1⁢A_s+g_0+g_1⁢V⁢T_sddtimeAbar_s=dAbar_s_dtddtimeA_s=dAbar_s_dt⁢alpha⁢L_m-Abar_s⁢L_m⁢VifV>0dAbar_s_dt⁢alpha⁢L_m+2⁢Abar_d-Abar_s⁢L_m⁢|V|ifV<0dAbar_s_dt⁢alpha⁢L_motherwisedTbar_s_dt=f⁢A_s+-g_0-g_1⁢V-k_minus_m⁢T_s+K_m⁢U_sddtimeTbar_s=dTbar_s_dtddtimeT_s=dTbar_s_dt⁢alpha⁢L_m-Tbar_s⁢L_m⁢VifV>0dTbar_s_dt⁢alpha⁢L_m+2⁢Tbar_d-Tbar_s⁢L_m⁢|V|ifV<0dTbar_s_dt⁢alpha⁢L_motherwisedUbar_s_dt=k_minus_m⁢T_s+-K_m-g_prime_0-g_prime_1⁢V⁢U_sddtimeUbar_s=dUbar_s_dtddtimeU_s=dUbar_s_dt⁢alpha⁢L_m-Ubar_s⁢L_m⁢VifV>0dUbar_s_dt⁢alpha⁢L_m+2⁢Ubar_d-Ubar_s⁢L_m⁢|V|ifV<0dUbar_s_dt⁢alpha⁢L_motherwise$

Component: double_overlap

$ddtimeRbar_d=-K_1⁢R_d+k_minus_1⁢A_d+g_prime_0+g_prime_1⁢V⁢U_dR_d=Rbar_d⁢alpha⁢L_mddtimeAbar_d=K_1⁢R_d+-f-k_minus_1⁢A_d+g_0+g_1⁢V⁢T_dA_d=Abar_d⁢alpha⁢L_mddtimeTbar_d=f⁢A_d+-g_0-g_1⁢V-k_minus_m⁢T_d+K_m⁢U_dT_d=Tbar_d⁢alpha⁢L_mddtimeUbar_d=k_minus_m⁢T_d+-K_m-g_prime_0-g_prime_1⁢V⁢U_dU_d=Ubar_d⁢alpha⁢L_m$

Component: calcium_flux

$I_o=Q_o⁢CaI_s=Q_s⁢1-ⅇ-timetau_SR⁢ⅇ-timetau_SF+I_l⁢Ca_0I_i=Q_i⁢1-ⅇ-timetau_iR⁢ⅇ-timetau_iF+I_l⁢Ca_rI_u=Q_u⁢CaK_mu+CaddtimeCa=I_s+I_i-I_o+I_u$

Component: bound_calcium

$BCa_L=A_s+T_s+A_d+T_d+A_nddtimeBCa_h=2⁢TRo-BCa_h⁢Ca⁢k_h-BCa_h⁢k_minus_h$

Component: force_equations

$F_CB=F_bar-eta⁢VF_CE=T_s+U_s⁢F_CBF_PE=E⁢ⅇD⁢SLSp_0-1-1+eta_PE⁢V_SLifSL≥Sp_0-B⁢1-SLSp_0+eta_PE⁢V_SLotherwiseF=F_CE+F_PE$

Component: input

$V=d_alpha_dt$
Source
Derived from workspace Landesberg, Sideman, 1994 at changeset 614313fee8ac.
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